Difficulty in understanding identifiability in the "Dueling Network Architectures for Deep Reinforcement Learning" paper
I believe that is explained on the prior page:

&quot;Intuitively, the value function $V$ measures the how good it is to be in a particular state $s$. The $Q$ function, however, measures the the value of choosing a particular action when in this state. The advantage function subtracts the value of the state from the $Q$
function to obtain a relative measure of the importance of
each action.&quot;

Then two paragraphs above were you started your quote:

&quot;However, we need to keep in mind that $Q(s, a; \theta, \alpha, \beta)$ is only a parameterized estimate of the true $Q$-function. Moreover, it would be wrong to conclude that $V (s; \theta, \beta)$ is a good estimator of the state-value function, or likewise that $A(s, a; \theta, \alpha)$ provides a reasonable estimate of the advantage function.
Equation (7) is unidentifiable in the sense that given $Q$ we cannot recover $V$ and $A$ uniquely. To see this, add a constant to $V (s; \theta, \beta)$ and subtract the same constant from $A(s, a; \theta, \alpha)$. This constant cancels out resulting in the same $Q$ value. This lack of identifiability is mirrored by poor practical performance when this equation is used directly.&quot;

Another way of looking at it would be:

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In a perfect world people could vote based on reputation, with a weighing based upon the correctness of the answer.
You could simply look at which answer received the most votes and choose it as correct.
In the real world things don't work that way, things are correct or incorrect whether they are measured or not (think quantum mechanics) and measurement doesn't always reveal the true answer.
See: Parameter Estimation.
The estimate of the advantage is only so good, sometimes it's useful to consider it and in other instances it's useful to reject it - intelligently doing both maximizes it's usefulness.